Siva,

There are 3 ways of interpreting your question. First, general relativity says that spacetime must have an average energy density of about 10^-9 J/m^3 to achieve the flat space. Cosmic observations show that space is flat to the experimental accuracy of about 1%. Therefore, the first implied energy density, confirmed by cosmic observation, is about 10^-9 J/m^3. The second implied vacuum energy density comes from quantum field theory (QFT). This requires the vacuum to have an extremely large energy density to achieve the incredible accuracy (correct to 10 significant figures) for some quantum mechanical calculations. For example, the QFT calculation of the electron’s anomalous magnetic dipole moment and the Lamb shift both require a very large energy density which implies Planck energy density (∿ 10^113 J/m^3) if we extrapolate zero-point energy to Planck frequency. This is a difference of about 10^122 but this is usually rounded off to 10^120. The name for this mystery is the “cosmological constant problem”. The third energy density for vacuum energy usually is between 10^40 and 10^60 J/m^3. This number depends on the assumptions required to achieve a particular quantum mechanical effect. In other words, this third energy density does not extrapolate to Planck frequency.

There have been over 250 papers written on the subject of the cosmological constant problem. This is one of the major mysteries of physics. The observable energy density of the vacuum is just 10^-9 J/m^3. However, the quantum mechanical requirements cannot be easily dismissed. Therefore, there is either a cancelation that has not been successfully explained or there is an unobservable form of energy which is actually in the vacuum. Planck length vacuum fluctuations might explain the required properties. This can give the vacuum constants of G, c and h bar while not generating its own gravity.

I am writing a paper on this subject. My approach is to analyze the properties of spacetime encountered by gravitational waves to determine the implied energy density of the vacuum. This approach is based on general relativity but it yields an answer which supports the large energy density predicted by QFT. This unobservable form of energy density is analyzed and modeled. This model makes interesting predictions.

This is known as the cosmological constant problem. Cosmological constant is a dimensionful quantity. It can be expressed in (GeV)4, so it is wiser to talk about ratios of two quantities in such cases where units cancel out. In this case for supersymmetric theories ∧theory/∧observed ~ 1060 where as for non-supersymmetric theories the ratio is 10120. Such a discrepancy between theory and observation usually leads to new theoretical developments. However, as you well know quantum gravity is an unknown theory and in very high energy scales, where gravity becomes comparable to other forces in terms of it's interaction strengths, naive expectations of quantum mechanics should not be taken very seriously.

You may read papers of Barrow and Shaw who has explained why the value of the cosmological constant is close to inverse square of the age of the universe in Planck units, that is ∧ ~ T -2

In my opinion, Quantum Field Theories are imperfect because these are perturbation theories. Same is true for Dirac’s theory and Quantum Electrodynamics. This is the reason when you try to extrapolate back to Planck epoch, they give erroneous results. Following quantum gravity theory gives you the correct energy density at the present epoch as well as at the Planck epoch and generates all the particles of the standard model from a single formula. In QFT, each of these particles have their own quantum field. Such considerations are not required in the period quantum gravity theory because the particles of the later epoch merge into the particles of the previous epoch as you go back and eventually only one particle field is left at the Planck epoch which has no more energy than of order 19. The equations of the theory fail to generate particles of higher order than the planck order. And at present epoch the Hubble parameter gives the precise value the cosmological constant. No quantum gravity theory or QFT is able to include Hubble parameter as part of non-perturbative formulation. This is because these theorists do not believe in periodic (quantized) nature of time.

Another important point is that the QFT calculation of the electron’s anomalous magnetic dipole moment and the Lamb shift are based on the false assumption in QED that virtual photons are responsible for these two effects requiring a very large energy density which implies Planck energy density (∿ 10^113 J/m^3) if we extrapolate zero-point energy to Planck frequency. Another article given here shows that virtual photons are not responsible for Lamb shift or 1s hyperfine structure of hydrogen atom. Dirac’s theory has ignored one quantum number xi discussed in this theory. Therefore Dirac’s theory cannot predict this effect and has to depend on virtual photons of QED which are not there in reality. The new theory given below uses Einstein’s field equations to explain Hydrogen spectra including Lamb shift and 1s Hyperfine structure from a single formula. This eliminates the need for the Quantum vacuum energy density predicted by QFT. So there is no problem with the cosmological constant, but the problem is the QFT problem.

https://www.researchgate.net/publication/262492889_Periodic_quantum_gravity_and_cosmology

https://www.researchgate.net/publication/319291737_Hydrogen_spectra_using_Einstein%27s_field_equations

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John Macken

I will try to follow you, since I am also agreeing the basic idea that every thing is related to energy of the space time.

Let me take some more time to study the 'cosmological constant problem'.

Thank you for your valuable explanations.

Biswajoy Brahmachari ,

Thank you for your feed back.Let us interact after few days on these matters...

QFT has many varieties in theory. It is not just one theory.